Comptes Rendus
no. 19-20
Lie Algebras/Mathematical Physics
On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, II
Michèle Vergne
Carlo A. Rossi1
1MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 871-874

We give a different proof of the famous result on compatibility between cup product (Kontsevich, 2003, [3, Section 8]) in cohomology of degree 0, for a finite-dimensional Lie algebra, from which we deduce an alternative way of re-writing Kontsevichʼs star product by means of the Alekseev–Torossian connection (Alekseev and Torossian, 2010, [1]).

On donne ici une preuve différente de la compatibilité entre cup produits (Kontsevich, 2003, [3, Section 8]) en cohomologie de degré 0 dans le cas dʼune algèbre de Lie de dimension finie, dʼoù on déduit, en utilisant la connection de Alekseev–Torossian (Alekseev et Torossian, 2010, [1]), une écriture alternative du produit-étoilé de Kontsevich.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.09.017

Carlo A. Rossi  1

1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany 
Carlo A. Rossi. On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, II. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 871-874. doi: 10.1016/j.crma.2012.09.017
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[1] A. Alekseev; C. Torossian Kontsevich deformation quantization and flat connections, Comm. Math. Phys., Volume 300 (2010) no. 1, pp. 47-64 | DOI

[2] M. Andler; S. Sahi; C. Torossian Convolution of invariant distributions: proof of the Kashiwara–Vergne conjecture, Lett. Math. Phys., Volume 69 (2004), pp. 177-203 | DOI

[3] M. Kontsevich Deformation quantization of Poisson manifolds, Lett. Math. Phys., Volume 66 (2003) no. 3, pp. 157-216

[4] C.A. Rossi On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, I, C. R. Acad. Sci. Paris, Sér. I, Volume 350 (2012) no. 17–18, pp. 823-826 | DOI

[5] B. Shoikhet Vanishing of the Kontsevich integrals of the wheels, Dijon (Lett. Math. Phys.), Volume 56 (2001) no. 2, pp. 141-149 | DOI

[6] C. Torossian Sur la conjecture combinatoire de Kashiwara–Vergne, J. Lie Theory, Volume 12 (2002) no. 2, pp. 597-616

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